I’m not a reviewer, so I have to pay for my own tickets, which is why I tend to go to see things I want to see, and why my reviews are usually so sycophantically positive. Occasionally, though, I splash out on something I know absolutely bugger all about, and am usually pleasantly surprised; last year, it was wee gems like Gretchen Parlato and, especially, Ane Brun. This year, it’s this mob.

Neil Cowley Trio’s album “The Face of Mount Molehill” is a bit of an oddity – a couple of jazz aficionado pals of mine aren’t too sure about it, calling it “prog rock jazz”. Well, stuff them; when I downloaded it a few weeks back in preparation for this gig, I loved those infectious banging chords and thumping rhythms. I can’t talk about this music with any sort of authority or from a position of knowledge or appreciation of jazz in general – but I know what I like.

And live, they are even better. Cowley is a magnificent pianist; there are numbers delicate enough for a conservatoire – the meandering perorations of “Skies are Rare”, for instance, are wistful and lovely, and “Slims” is just the simplest and yet most elegant of jazz melodies – but he can also bang all the percussive potential out of his instrument if he has to; their second album is called “Loud…Louder… Stop!”, which just about sums them up. As with all excellent pianists, his hands on the keyboard are a thing of beauty.

And what a tight, tight band this is. Rex Horan (a man who possesses the finest head of hair in the music business, and I mean everything above the neck) on double bass and Evan Jenkins on drums are brilliant, and they obviously like working with Cowley so much, they are all almost telepathic in some of their seemingly random, thrashed entries, banging out staccato chords that seem to take them all by surprise and yet are all perfectly timed.

Listen, this was great. Tracks like “Fable” and “Rooster was a Witness” are as exciting as bungee jumping (not that I’ve ever bungee jumped) and the encore number, “She Eats Flies” is just damned well epic. Apparently, it’s about a spider that lives at the bottom of his garden that, he says, is as big as a cat; judging by the noise they make about it, I believe him, and there is no fucking way on earth I’m going anywhere near his garden.

Cowley’s also very personable (“You can dance to this if you have a limp”) and down to earth; he likes the Glasgow Festival because it’s the least jazzy jazz festival he knows, which he reckons is a good thing. I’ll go along with that; I’m still not sure if I like “jazz”, but I sure as hell like this. Great stuff.

Well, Ana Moura, yet another flashing-eyed fadista I’ve wanted to see live for some time, was everything I hoped she’d be, and a whole lot more.

Let’s get the obvious adolescent boy stuff out of the way first. She is one of the most beautiful women I’ve ever seen. Dressed in a stunning black sequined and lace evening dress, she shimmers and explodes like a firework when she catches the light: “she’s like a mermaid,” my sister says. Indeed she is: a fabled, fabulous creature.

She’s much more self contained than many of the fadistas I’ve seen before; singers like Ana Bacalhau or Mariza throw themselves dramatically into the song, physically grabbing it by the throat. Moura’s style involves the merest swing of the hips, the drop of a shoulder, an inclination of the head, and the effect is just as mesmerising, just as sensual. She is utterly elegant.

But of course the star of the show is that voice, a lusty contralto that is capable of breathy subtlety, heart-rending sorrow or barnstorming joy, and Pedro, Angel and Phillippe provide the impeccable backdrop a voice of this quality deserves. Whenever I listen to fado, I’m transported to orange groves and beaches strewn with fishing boats and whitewashed villages where love is rampant and hearts are broken every day. It’s gorgeous. She sings songs mainly from her new live album, “Coliseu”, and songs like “Os Meus Olhos São Dois Círios” or “Sou Do Fado, Sou Fadista” certainly do it for me. Get it, listen to it, fall in love with it.

The second act is one of those weird combinations Celtic Connections delights in encouraging; if you thought teuchter salsa was odd, N’Diale combine the Breton Jackie Molard Quartet with the Foune Diarra trio from Mali. There’s no doubt these are fantastic musicians, but it doesn’t quite hit the spot for me. The Malian desert blues is great, and the set is at its most successful when the n’goni and the drum and Diarra’s beautiful voice are foregrounded. However, the Celtic jigs and reels bolted on seem a little irrelevant, while some of the contributions from the western instruments – bass and sax solos that are more like jazz than anything – are just a bit… well… self-indulgent. This is obviously really accomplished music, and I admired it: I just didn’t feel it, and while I wanted to hear songs, at times I felt I was listening to compositions. The audience too seem to drift, the enormous goodwill that flowed towards Moura turning into something more polite and reserved.

Along with quite a few others, we left early – work commitments tomorrow! – so perhaps N’Diale (which means, rather sweetly, ‘the pleasure of being together’) hotted up the house. I hope so.

Meanwhile, I’m off to sleep, and hopefully dream of fantastically beautiful dark mermaids who can sing my soul to life.